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origin of any social regulation on the subject. Such a regulation did not arise in any contemplation of benefit to the lenders of money. On the contrary, they, being the sinewy men of war and peace, were very well able to take care of themselves without law, as some are even said to do to this day in spite of it; it was needed for the borrowers. The very admission of a limit, makes this evident without argument. Now there may be and often are cases of limits being set in theory which are very far from being carried out in practice, but
we are not warranted in supposing any law-makers to contemplate a frustration in theory of their own limit; such as will occur by any other method of computation for interest than the one that has been indicated. Whether then we trace the origin and type of our usury laws (so far as England is concerned) to the Dano-Saxon period when borrowers, although in the Council and in the Field among the mighty of the land, were, as respected the demand for re-payment and for the use of the loan, at the mercy of the lenders; or look for it three centuries later when the growing commerce of the Hanse-Towns, and the difficulties of actual exchanges had created a new class of what may be termed involuntary debtors (merchants having balances of their correspondents in their hands but without ready or safe means of remittance ;) we are equally authorized in saying that the imposition of a limit was for the protection of the borrower.
Such protection when the theory of the law is carried out would be afforded both directly and indirectly; directly in the uniformity of the rate of charge for interest; and indirectly, because if the money lender could get no more than 106 for the 100 at the end of the year no matter how often he renewed the loan or turned his money over, he would be preserved from the temptation of seeking short investments in order to force quick returns. And on the other hand, while this was perfectly just towards the other party in the financial result, it recognized besides a principal of importance, viz: that his interest was necessarily accruing as well for the least as the larger intervals of time.
All this is apparent upon the mere inspection of the formula* according to which calculations for interest are made. It will be more evident by the following table showing, with the same rate of 6 per cent. per annum and a true year of 3654 days, the interest in cents and hundredils on a capital of 100 dollars for the days specified in the margin respectively and a farther allowance of three days grace; by the legal, and also by the habitual method.
* For the case of continuous or as it is generally termed compound interest where the rate is uniform, the expression is a = A. 1+r.";r being the rate per cent. per annum and a being the aggregate of principal and interest on a capital A placed for the term n, an integral or proportional part of a year. If n is in days, the ex. pression becomes
for the true year. a=A. 1+1 In the case of ordinary method of calculation, the expression is
a= A1+ nr. the symbols retaining the same signification as before.
Days specified in Interest habitually Interest reckoned upon the the obligation.
presumed theory of the law.
596,20 It is apparent here that the computations of the last column give a less amount for interest than those of the second, and this in proportion as the period becomes smaller and smaller; while they both coincide at the end of the year. Jf, then, it be only admitted that the law purposed a mode of computation which should be most advantageous to the borrower (as seems, from what has been already said, highly probable) it may be affirmed without regard to any other consideration, that the method adopted in the last column is the one which fulfils the aim of the law. And if regard be had to the other considerations, it may be repeated that this method, resulting at the end of the year in just the aggregate that the law prescribes, is the only method in which such an aggregate can be computed with an uniform rate of interest at any and all periods of the year. The other, habitual mode must be confessed to correspond with no explicable motive in the law; and, not based upon any proper technical idea of ratio, destroys all uniformity of rate. Such uniformity, at least, we may presume it was the aim of the law to inspire and maintain ; and in so far as it is not maintained, the aim is proportionally frustrated.
Again the scope of the law is very marked in prohibiting the charge of interest upon interest. This prohibition was intended, it may be presumed, to refer to such a charge directly; for an indirect charge, such as is made by the method indicated here as the proper one, was, it is very probable, hardly appreciated by the legislators at the time. If it was, it would most likely have been adopted in terms; at all events it would have been equally in terms forbidden. But however this may be, the habitual practice always admits, indeed necessitates a direct accrual of interest upon interest even when the interest is not required to be paid in advance, whenever the term of the loan is less than one year. "Now it will be said that although interest does so accrue, it is not so charged to any borrower; and that the prohibition is against charging not accruing. But an answer like this takes a very limited view of social and moral obligations. All along, there has been good reason for supposing that usury-laws were made for the benefit of the borrowers, and if so, of course to tie up
the lenders. But even if this be incorrect, there is no process of ethical or historical proof to shew that such laws were made for the lenders' benefit; and the utmost that could be claimed would be that it was intended to bear equally on both parties.
Now an equality without an equation is what no one, mathematician, lawyer or layman can understand; and yet such would be the category if the lender be not as much bound not to receive as
the borrower is justified not to pay. When the law forbids A. to charge B. interest upon interest or interest above a certain rate, it was not in the view of its being too much for B. to pay but too much for A. to receive, as is apparent from the whole scope of the penalties imposed in this regard; all of which fall on A. not on B. If then the excessive interest be too much for A. to receive from B, it is too much for him to receive from C. or D. or any other designation in the alphabet. And yet he does so receive it whenever a loan is made for a less period than a year. This will be evident from the following table which shows the improvement in one year at 6 per cent. per annum of a capital of 1 dollar or other unitary coin at simple interest as it is termed, when it is turned over successively immediately for all the periods less than a year, specified below. When the period is for a year there is of course a conformity with the legal rate. As this table is only for illustration, the year is taken as if it were 360 days; and the computation is for the net days specified.
Amount of Principal Periods of Improvt Amount improved at Formula for and Continuous Inin Days. the end of the year.
Simple Interest. terest at the end of
1 360 days
1,014674 1,015 1,061521 1,010
12 1,061678 1,005
1,001620 The second column of this table shews the want of uniformity in the amount of annual interest accruing upon a constant capital placed at various periods, according to the ordinary computation. Thus the annual interest, which if placed for a year is 6 per centum, becomes, when the capital is lent from four to four months, nearly 64 per centum; if placed from inonth to month, the annual interest is more than 64 per cent. The next column is given to indicate the form of computation for the preceding; and to shew that what is usually termed simple interest, is in fact compounded upon both principal and the periodical interest. The last column shews the aggregate of principal and interest at the end of each corresponding period, when the interest is continually converted into principal as it arises, at a constant rate, for any term however long or short, of 6 per cent. per annum. To this kind of computation the name of compound interest has been usually given; it should rather be called continuous interest. The true compound interest or interest upon interest directly, occurs in the habitual method as shewn in the third column. It is hardly necessary to repeat that while this last goes on in an augmenting annual rate according to the frequency of re-investment; the other maintains its rate constant, no matter how
frequently or how seldom the loan is renewed; were there a fresh placement every hour in the day and night (or 8766 renewals in the course of the year,) the capital that was 100 at the beginning could be only 106 at the end of the year. So the aggregate, which at the expiration of 10 days was 100,16 zo very nearly, after 17 renewals for a similar period will become only 102,95f nearly; and so on.
The augmentation in the rate of interest, which, as has been seen, takes place according to the other method of compounding and which goes on increasing, has nevertheless, as might be supposed, a maximum limit which it cannot transcend. In fact, this limit occurs when the period of placement is infinitely small; the amount improved becomes then 1,061837, very nearly, or what is the same thing the annuity of the interest reaches 636 per cent. nearly. Of course when the period for improvement becomes actually zero, the improvement itself is nothing, and its amount, null.*
Such then are the principal indications shewing the systematic frusIration of the intent of the law in the habitual mode of computing interest. It is not necessary to dwell on the practice of requiring interest to be paid in advance nor to exhibit its numerical results; it will be admitted that it conduces to a gain for the lender which, however justified by usage, is not countenanced by the law. It is true that this practice has come to be disguised, (however unconsciously) under another name, that of discount ; and, in so far, is still another deviation from original acceptations. Discount, as the word at first signified among the people from whom we have borrowed it, and as still understood by Cambists, is a deduction made from a principal sum, either, 10 in exchanges, to equalize different sorts of money between two parties, respectively; or, 20 in re-payments, when a loan is returned before the stipulated period. In the first case, the rate is for convenience reckoned at so much per cent upon one or the other kind of money in question. According as the better or worse money is regarded as the standard of comparison, it bears the name of agio or discount. But in no degree has it any relation with interest; for it has nothing to do with the use of money or as loan. In the second case, a creditor may, according to circumstances, allow more or less in order to regain possession at once of money lent for a period yet to elapse. This is analogous to the allowance for cash payment technically, the rebate) made in the purchase of articles usually sold on a credit. But it is evident that all such allowances are irrespective of Interest properly so understood.
• It is to a case of this sort that the properties of logarithmic curves find their application ; which Milne, for instance, and others have erroneously attributed to the case of continuous or, as it is sometimes called, incessant interest. The limit given in the text is very readily found by transferring the number representing the annual rate of interest froin the ordinary series of logarithms, whose modulus (or the subtangent of the curve) is 0,43429 etc. to that in which the modulus is 1. This last is the Napierian or (as it is very often, but improperly, called) the hyperbolic system; whose first term, when the differential is infinitely small, is of the same form with the differential of the expression for interest. But it does not apply to the case of continuous interest; whose expression 1 + " "; analogous to zo becomes, when n= ), 2° = 1; i. e. a constant quantity; in other words, when there is no period of place. ment, the principal remains constant, which is exactly what would be concluded without the aid of mathematical apparatus.
RESUMPTION IN MARYLAND. The following correspondence has been published in the daily papers of Baltimore. It will demonstrate the influence exerted by Mr. Speed and Mr. Peabody in bringing about a resumption of payment on its public debt by Maryland. Letter from Gov. Thomas to J. J. Speed, Esq.
State DeparTMENT, >
Annapolis, 20th October, 1848. ) My Dear Sir:-You were good enough, at my request, to consent to take charge of the resolutions of the General Assembly, refering, in complimentary terms, to the conduct of Mr. George Peabody, in connexion with the public debt of the State, and to forward them as soon as received, by some safe conveyance to London. I have now the pleasure to place in your hands, these resolutions, together with a letter from myself, drawn in such terms as I conceived to be appropriate, and in conformity to what I suppose was the intention of the Legislature as expressed in the last of the resolutions. I also herewith inclose, copies of both these papers, to be used as you may think proper. For your kindness in undertaking to cause them to be transmitted, you will be pleased to accept my thanks.
I am, dear sir, your obliged and ob't serv't, Philip F. THOMAS. J. J. SPEED, Esq.
Resolutions of the Legislature of Maryland. BY THE HOUSE OF Delegates, March 7th, 1848.
Whereas, Mr. George Peabody, a citizen of Maryland, now resident of London, was appointed one of three Commissioners, under the act of Assembly, of eighteen hundred and thirty-five, to negotiate a loan for this State, and after performing the duties assigned to him, refused to apply for the compensation allowed by the provisions of that ach, because he was unwilling to add to the burthens of the State, at a time when she was overwhelmed with the weight of her obligations; And whereas, since the credit of the State has been restored, he has voluntarily relinquished all claim for the compensation due to him for his services, expressing himself fully paid by the gratification of seeing the State freed from reproach in the eyes of the world.
Be it unanimously resolved by the General Assembly of Maryland, That the record of such disinterested zeal, is higher praise than any that eloquence could bestow, and that this Legislature is therefore content with tendering the thanks of this State to Mr. Peabody, for his generous devotion to the interests and honor of Maryland.
And further resolved, That the Governor of this State be requested to transmit these Resolutions to Mr. Peabody, in such manner as he may deem most appropriate. By order, Geo. G. BREWER, Clerk. By The Senate, March 8th, 1848. Read and assented to. By order, Jos. H. NICHOLSON, Clerk. True copy-Test,
Rich'd W. Gill, Clerk Court of Appeals, W. S.